Lie Groups #1 - Introduction + The General Linear group GL(n, R)

This video will introduce the concept of a Lie group, realised as a continuous group that also has the structure of a smooth manifold (see my manifold lectures for more, I will assume you have some idea about what a manifold is in this video).

I will mostly be relying on examples rather than formal definitions to begin with, and this video covers the most general Lie group, the general linear group. I discuss how we realise this matrix group as a manifold (by constructing charts, effectively the matrix elements are the coordinates).

If you like my videos and want to consider supporting the channel I am now accepting donations in DOGE and BTC (other cryptos on request) See my channel description for the addresses!

[sietsebuijsman]

I once again have a question and I'm sorry if it's a bit pedantic. But if the determinant of the matrix cannot be zero, that must mean there exist many combinations a, b, c and d (or more for higher n of course) that are excluded from this R^n² space. So then does this space sort of have "holes" in it? And is this a significant detail at all?

[mehedifaysal]

didn't know that Joffrey Baratheon will teach me about Lie group

[AtmosMr]

"proof by waving my hands." Like it! :) I do that a lot too.

[FlaxbrookStudios]

I really appreciate the brevity and digestibility of these videos. As someone who just wants to learn abstract algebra concepts for practical reasons and not necessarily practice it in a formal academic setting.

[bernardofitzpatrick]

Ure dog must be a genius mathematician by now. 😀 great explanation. 👏

[profezmo]

way more clear than the other videos I tried, thanks for posting this

[BCarli]

Thank you. It’s very helpful at times to dispense with formal definitions.

[pairadeau]

As an aside, I'm not sure if you were aware of how difficult your channel is to find via a cursory search of the channel name on youtube. The channel is extremely warm and inviting and it's a shame that youtube hides it so deeply within the algorithm.

[ncclelland]

Hello, really great videos. Your intuition based way of teaching is really helpful (the manifold videos were especially good). Not sure if this is something you'd be interested in but Eric Weinstein (mathematics PHD working with Peter Thiel) is building a community to crowdsource information regarding mathematics, geometry and physics. His project is called The Portal. I think they would really welcome someone with your skillset. All the best.

[muzammilaziz]

Jack Gleeson left acting and now teaches Lie Groups on YouTube. Great

[wowlikefun]

thanks for these nice lie group series! It is so helpful that instead of mathematical rigor, you're focusing on providing and intuition, totally love that! It would be helpful to see the similar set of lectures but just for group theory.

[SiiKiiN]

Loved the video, the wobbling is a bit distracting especially at when watch at 1.5 speed

[farhanrafid]

You can open Patreon where people will support you like crazy

[allyburlesque]

"proof by handwaving" :D :D Hope my Prof. will be ok with that, too :D hahaha

[jacobvandijk]

Apart from continuous symmetries there are discrete symmetries. Is there a reason why you only discuss the continuous ones?

[piyalikarmakar]

what's the meaning of all those decorations? is it christmas special lmao? But what's that dog I mean seriously dogs and lights in a maths video!!!!

[tobiashoek]

Nice video but could you please stand still?

[tedsheridan]

Good content but please stop dancing while you speak.